#521242 (C++17) No.1145 Sums of Powers

• 問題: No.1145 Sums of Powers
• ユーザー: hotman78
• 提出日時: 2020-07-31 21:25:44
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 1,093 ms / 2,000 ms
• コード長: 14,641 bytes
• コンパイル時間: 7,734 ms
• コンパイル使用メモリ: 434,620 KB
• 実行使用メモリ: 71,608 KB
• 最終ジャッジ日時: 2024-07-06 16:15:22
• 合計ジャッジ時間: 12,129 ms
• ジャッジサーバーID （参考情報）: judge2 / judge1

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 5,248 KB
testcase_01	AC	2 ms; 5,248 KB
testcase_02	AC	9 ms; 5,376 KB
testcase_03	AC	1,093 ms; 71,596 KB
testcase_04	AC	1,089 ms; 71,600 KB
testcase_05	AC	1,090 ms; 71,608 KB

コンパイルメッセージ

main.cpp:51:22: warning: use of 'auto' in parameter declaration only available with '-std=c++20' or '-fconcepts'
   51 | inline auto reversed(auto v){reverse(v.begin(),v.end());return v;}
      |                      ^~~~
main.cpp:58:12: warning: use of 'auto' in parameter declaration only available with '-std=c++20' or '-fconcepts'
   58 | bool chmin(auto& s,const auto& t){bool res=s>t;s=min(s,t);return res;}
      |            ^~~~
main.cpp:58:26: warning: use of 'auto' in parameter declaration only available with '-std=c++20' or '-fconcepts'
   58 | bool chmin(auto& s,const auto& t){bool res=s>t;s=min(s,t);return res;}
      |                          ^~~~
main.cpp:59:12: warning: use of 'auto' in parameter declaration only available with '-std=c++20' or '-fconcepts'
   59 | bool chmax(auto& s,const auto& t){bool res=s<t;s=max(s,t);return res;}
      |            ^~~~
main.cpp:59:26: warning: use of 'auto' in parameter declaration only available with '-std=c++20' or '-fconcepts'
   59 | bool chmax(auto& s,const auto& t){bool res=s<t;s=max(s,t);return res;}
      |                          ^~~~

ソースコード

#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC push_options
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx")
#include<bits/stdc++.h>
#include <xmmintrin.h>
#include <immintrin.h>
using namespace::std;
__attribute__((constructor))void init(){cin.tie(0);ios::sync_with_stdio(false);cout<<fixed<<setprecision(15);}
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/priority_queue.hpp>
#include<ext/pb_ds/tag_and_trait.hpp>
// #include <boost/multiprecision/cpp_dec_float.hpp>
// #include <boost/multiprecision/cpp_int.hpp>
// namespace mp = boost::multiprecision;
// typedef mp::number<mp::cpp_dec_float<0>> cdouble;
// typedef mp::cpp_int cint;
template<typename T>using pbds=__gnu_pbds::tree<T,__gnu_pbds::null_type,less<T>,__gnu_pbds::rb_tree_tag,__gnu_pbds::tree_order_statistics_node_update>;
template<typename T>using pbds_map=__gnu_pbds::tree<T,T,less<T>,__gnu_pbds::rb_tree_tag,__gnu_pbds::tree_order_statistics_node_update>;
template<typename T,typename E>using hash_map=__gnu_pbds::gp_hash_table<T,E>;
template<typename T>using pqueue =__gnu_pbds::priority_queue<T, greater<T>,__gnu_pbds::rc_binomial_heap_tag>;
typedef long long lint;
#define INF (1LL<<60)
#define IINF (1<<30)
#define LINF (9223372036854775807LL)
#define EPS (1e-10)
#define endl ('\n')
//#define MOD 1000000007LL
#define MOD 998244353LL
//#define MOD 18446744069414584321ULL
typedef vector<lint> vec;
typedef vector<vector<lint>> mat;
typedef vector<vector<vector<lint>>> mat3;
typedef vector<string> svec;
typedef vector<vector<string>> smat;
template<typename T>inline void numout(T t){bool f=0;for(auto i:t){cout<<(f?" ":"")<<i<INF/2?i:"INF";f=1;}cout<<endl;}
template<typename T>inline void numout2(T t){for(auto i:t)numout(i);}
template<typename T>inline void output(T t){bool f=0;for(auto i:t){cout<<(f?" ":"")<<i;f=1;}cout<<endl;}
template<typename T>inline void output2(T t){for(auto i:t)output(i);}
template<typename T>inline void _output(T t){bool f=0;for(lint i=0;i<t.size();i++){cout<<f?"":" "<<t[i];f=1;}cout<<endl;}
template<typename T>inline void _output2(T t){for(lint i=0;i<t.size();i++)output(t[i]);}
#define rep(i,...) for(auto i:range(__VA_ARGS__)) 
#define rrep(i,...) for(auto i:reversed(range(__VA_ARGS__)))
#define repi(i,a,b) for(lint i=lint(a);i<(lint)(b);++i)
#define rrepi(i,a,b) for(lint i=lint(b)-1;i>=lint(a);--i)
#define irep(i) for(lint i=0;;++i)
inline vector<int64_t> range(int64_t n){vector<int64_t>v(n);iota(v.begin(),v.end(),0LL);return v;}
inline vector<int64_t> range(int64_t a,int64_t b){vector<int64_t>v(b-a);iota(v.begin(),v.end(),a);return v;}
inline vector<int64_t> range(int64_t a,int64_t b,int64_t c){vector<int64_t>v((b-a+c-1)/c);for(int i=0;i<(int)v.size();++i)v[i]=i?v[i-1]+c:a;return v;}
inline auto reversed(auto v){reverse(v.begin(),v.end());return v;}
#define all(n) begin(n),end(n)
#define dist(a,b,c,d) sqrt(pow(a-c,2)+pow(b-d,2))
//inline lint gcd(lint A,lint B){return B?gcd(B,A%B):A;}
//inline lint lcm(lint A,lint B){return A/gcd(A,B)*B;}
// inline cint cgcd(cint A,cint B){return B?cgcd(B,A%B):A;}
// inline cint clcm(cint A,cint B){return A/cgcd(A,B)*B;}
bool chmin(auto& s,const auto& t){bool res=s>t;s=min(s,t);return res;}
bool chmax(auto& s,const auto& t){bool res=s<t;s=max(s,t);return res;}
const vector<lint> dx={1,0,-1,0,1,1,-1,-1};
const vector<lint> dy={0,1,0,-1,1,-1,1,-1};
#define SUM(v) accumulate(all(v),0LL)
auto call=[](auto f,auto... args){return f(f,args...);};
template<typename T,typename ...Args>auto make_vector(T x,int arg,Args ...args){if constexpr(sizeof...(args)==0)return vector<T>(arg,x);else return vector(arg,make_vector<T>(x,args...));}

template<typename T,typename P>
struct FPS_BASE:vector<T>{
    using vector<T>::vector;
    inline P operator +(T x)noexcept{return P(*static_cast<P*>(this))+=x;}
    inline P operator -(T x)noexcept{return P(*static_cast<P*>(this))-=x;}
    inline P operator *(T x)noexcept{return P(*static_cast<P*>(this))*=x;}
    inline P operator /(T x)noexcept{return P(*static_cast<P*>(this))/=x;}
    inline P operator <<(int x)noexcept{return P(*static_cast<P*>(this))<<=x;}
    inline P operator >>(int x)noexcept{return P(*static_cast<P*>(this))>>=x;}
    inline P operator +(const P& x)noexcept{return P(*static_cast<P*>(this))+=x;}
    inline P operator -(const P& x)noexcept{return P(*static_cast<P*>(this))-=x;}
    inline P operator -()noexcept{return P(1,T(0))-=P(*static_cast<P*>(this));}
    inline P operator *(const P& x)noexcept{return P(*static_cast<P*>(this))*=x;}
    inline P operator /(const P& x)noexcept{return P(*static_cast<P*>(this))/=x;}
    inline P operator %(const P& x)noexcept{return P(*static_cast<P*>(this))%=x;}
    inline P &operator +=(T x){
        if(this->size()==0)this->resize(1,T(0));
        (*static_cast<P*>(this))[0]+=x;
        return (*static_cast<P*>(this));
    }
    inline P &operator -=(T x){
        if(this->size()==0)this->resize(1,T(0));
        (*static_cast<P*>(this))[0]-=x;
        return (*static_cast<P*>(this));
    }
    inline P &operator *=(T x){
        for(int i=0;i<(int)this->size();++i){
            (*static_cast<P*>(this))[i]*=x;
        }
        return (*static_cast<P*>(this));
    }
    inline P &operator /=(T x){
        return (*static_cast<P*>(this))*=(T(1)/x);
    }
    inline P &operator <<=(int x){
        P ret(x,T(0));
        ret.insert(ret.end(),begin(*static_cast<P*>(this)),end(*static_cast<P*>(this)));
        return (*static_cast<P*>(this))=ret;
    }
    inline P &operator >>=(int x){
        P ret;
        ret.insert(ret.end(),begin(*static_cast<P*>(this))+x,end(*static_cast<P*>(this)));
        return (*static_cast<P*>(this))=ret;
    }
    inline P &operator +=(const P& x){
        if(this->size()<x.size())this->resize(x.size(),T(0));
        for(int i=0;i<(int)x.size();++i){
            (*this)[i]+=x[i];
        }
        return (*static_cast<P*>(this));
    }
    inline P &operator -=(const P& x){
        if(this->size()<x.size())this->resize(x.size(),T(0));
        for(int i=0;i<(int)x.size();++i){
            (*static_cast<P*>(this))[i]-=x[i];
        }
        return (*static_cast<P*>(this));
    }
    inline P &operator *=(const P& x){
        return (*static_cast<P*>(this))=mul((*static_cast<P*>(this)),x);
    }
    inline P &operator /=(P x){
        if(this->size()<x.size()) {
            this->clear();
            return (*static_cast<P*>(this));
        }
        const int n=this->size()-x.size()+1;
        return (*static_cast<P*>(this)) = (rev().pre(n)*x.rev().inv(n)).pre(n).rev(n);
    }
    inline P &operator %=(const P& x){
        return ((*static_cast<P*>(this))-=*static_cast<P*>(this)/x*x);
    }
    inline P& shrink(){while((*static_cast<P*>(this)).back()==0)(*static_cast<P*>(this)).pop_back();return (*static_cast<P*>(this));}
    inline P pre(int sz)const{
        return P(begin(*this),begin(*this)+min((int)this->size(),sz));
    }
    inline P rev(int deg=-1){
        P ret(*static_cast<P*>(this));
        if(deg!=-1)ret.resize(deg,T(0));
        reverse(begin(ret),end(ret));
        return ret;
    }
    P inv(int deg=-1){
        assert((*static_cast<P*>(this))[0]!=T(0));
        const int n=deg==-1?this->size():deg;
        P ret({T(1)/(*this)[0]});
        for(int i=1;i<n;i<<=1){
            ret=(ret*T(2)-ret*ret*pre(i<<1)).pre(i<<1);
        }
        return ret.pre(n);
    }
    inline P dot(const P& x){
        P ret(*static_cast<P*>(this));
        for(int i=0;i<int(min(this->size(),x.size()));++i){
            ret[i]*=x[i];
        }
        return ret;
    }
    P diff(){
        P ret(*static_cast<P*>(this));
        for(int i=0;i<(int)ret.size();i++){
            ret[i]*=i;
        }
        return ret>>1;
    }
    P integral(){
        P ret(*static_cast<P*>(this));
        for(int i=0;i<(int)ret.size();i++){
            ret[i]/=i+1;
        }
        return ret<<1;
    }
    P log(int deg=-1){
        assert((*this)[0]==T(1));
        const int n=deg==-1?this->size():deg;
        return (diff()*inv(n)).pre(n-1).integral();
    }
    P exp(int deg=-1){
        assert((*this)[0]==T(0));
        const int n=deg==-1?this->size():deg;
        P ret({T(1)});
        for(int i=1;i<n;i<<=1){
            ret=ret*(pre(i<<1)+1-ret.log(i<<1)).pre(i<<1);
        }
        return ret.pre(n);
    }
    P sqrt(int deg=-1){
        const int n=deg==-1?this->size():deg;
        if((*this)[0]==T(0)) {
            for(int i=1;i<(int)this->size();i++) {
                if((*this)[i]!=T(0)) {
                    if(i&1)return{};
                    if(n-i/2<=0)break;
                    auto ret=(*this>>i).sqrt(n-i/2)<<(i/2);
                    if((int)ret.size()<n)ret.resize(n,T(0));
                    return ret;
                }
            }
            return P(n,0);
        }
        P ret({T(1)});
        for(int i=1;i<n;i<<=1){
            ret=(ret+pre(i<<1)*ret.inv(i<<1)).pre(i<<1)/T(2);
        }
        return ret.pre(n);
    }
    T eval(T x){
        T res=0;
        for(int i=(int)this->size()-1;i>=0;--i){
            res*=x;
            res+=(*this)[i];
        }
        return res;
    }
    vector<T> multipoint_eval(const vector<T>&x){
        const int n=x.size();
        P* v=new P[2*n-1];
        for(int i=0;i<n;i++)v[i+n-1]={T()-x[i],T(1)};
        for(int i=n-2;i>=0;i--){v[i]=v[i*2+1]*v[i*2+2];}
        v[0]=P(*static_cast<P*>(this))%v[0];v[0].shrink();
        for(int i=1;i<n*2-1;i++){
            v[i]=v[(i-1)/2]%v[i];
            v[i].shrink();
        }
        vector<T>res(n);
        for(int i=0;i<n;i++)res[i]=v[i+n-1][0];
        return res;
    }
    virtual P mul(P s,P t)=0;
};


template<typename Mint>
struct fps9:FPS_BASE<Mint,fps9<Mint>>{
    using FPS_BASE<Mint,fps9<Mint>>::FPS_BASE;
    using P=fps9<Mint>;
    P mul(P s,P t)override{
        const int n=s.size()+t.size()-1;
        int h=1;
        while((1<<h)<n)h++;
        s.resize((1<<h),Mint(0));
        t.resize((1<<h),Mint(0));
        return ntt(ntt(s,h,0).dot(ntt(t,h,0)),h,1).pre(n);
    }
    P ntt(P v,const int& h,const bool& inv){
		const int n=v.size();
        assert(Mint::get_mod()>=3&&Mint::get_mod()%2==1);
		P tmp(n,Mint());
        Mint root=inv?Mint(Mint::root()).inv():Mint::root();
        for(int b=n>>1;b>=1;b>>=1,v.swap(tmp)){
            Mint w=root.pow((Mint::get_mod()-1)/(n/b)),p=1;
            for(int i=0;i<n;i+=b*2,p*=w)for(int j=0;j<b;++j){
                v[i+j+b]*=p;
                tmp[i/2+j]=v[i+j]+v[i+b+j];
                tmp[n/2+i/2+j]=v[i+j]-v[i+b+j];
            }
        }
        if(inv)v/=n;
        return v;
	}
};

class mint {
  using u64 = std::uint_fast64_t;
    public:
    u64 a;
    constexpr mint(const long long x = 0)noexcept:a(x>=0?x%get_mod():get_mod()-(-x)%get_mod()){}
    constexpr u64 &value()noexcept{return a;}
    constexpr const u64 &value() const noexcept {return a;}
    constexpr mint operator+(const mint rhs)const noexcept{return mint(*this) += rhs;}
    constexpr mint operator-(const mint rhs)const noexcept{return mint(*this)-=rhs;}
    constexpr mint operator*(const mint rhs) const noexcept {return mint(*this) *= rhs;}
    constexpr mint operator/(const mint rhs) const noexcept {return mint(*this) /= rhs;}
    constexpr mint &operator+=(const mint rhs) noexcept {
        a += rhs.a;
        if (a >= get_mod())a -= get_mod();
        return *this;
    }
    constexpr mint &operator-=(const mint rhs) noexcept {
        if (a<rhs.a)a += get_mod();
        a -= rhs.a;
        return *this;
    }
    constexpr mint &operator*=(const mint rhs) noexcept {
        a = a * rhs.a % get_mod();
        return *this;
    }
    constexpr mint operator++(int n) noexcept {
        a += 1;
        if (a >= get_mod())a -= get_mod();
        return *this;
    }
    constexpr mint operator--(int n) noexcept {
        if (a<1)a += get_mod();
        a -= 1;
        return *this;
    }
    constexpr pair<int, int> extgcd(int a, int b) {
        int s = a, sx = 1, sy = 0, t = b, tx = 0, ty = 1;
        while (s % t != 0) {

            int temp = s / t;
            int u = s - t * temp;
            int ux = sx - tx * temp;
            int uy = sy - ty * temp;

            s = t;
            sx = tx;
            sy = ty;
            t = u;
            tx = ux;
            ty = uy;
        }
        return {tx, ty};
    }
    constexpr mint &operator/=(mint rhs) noexcept {
        return (*this)*=mint(extgcd(rhs.a,get_mod()).first);
    }
    constexpr bool operator==(mint x) noexcept {
        return a==x.a;
    }
    constexpr bool operator!=(mint x) noexcept {
        return a!=x.a;
    }
    constexpr static int root(){
        mint root = 2;
        while(root.pow((get_mod()-1)>>1).a==1)root++;
        return root.a;
    }
    constexpr mint pow(long long n){
        long long x=a;
        mint ret = 1;
        while(n>0) {
            if(n&1)(ret*=x);
            (x*=x)%=get_mod();
            n>>=1;
        }
        return ret;
    }
    constexpr mint inv(){
        return pow(get_mod()-2);
    }
    static vector<mint> fac,ifac;
    static bool init;
    constexpr static int mx=10000001;
    void build(){
        init=0;
        fac.resize(mx);
        ifac.resize(mx);
        fac[0]=1,ifac[0]=1;
        for(int i=1;i<mx;i++)fac[i]=fac[i-1]*i;
        ifac[mx-1]=fac[mx-1].inv();
        for(int i=mx-2;i>=0;i--)ifac[i]=ifac[i+1]*(i+1);
    }
    mint comb(lint b){
        if(init)build();
        if(a==0&&b==0)return 1;
        if((lint)a<b||a<0)return 0;
        return fac[a]*ifac[a-b]*ifac[b];
    }
    mint fact(){
        if(init)build();
        return fac[a];
    }
    mint fact_inv(){
        if(init)build();
        return ifac[a];
    }
    friend ostream& operator<<(ostream& lhs, const mint& rhs) noexcept {
        lhs << rhs.a;
        return lhs;
    }
    friend istream& operator>>(istream& lhs,mint& rhs) noexcept {
        lhs >> rhs.a;
        return lhs;
    }
    constexpr static u64 get_mod(){return MOD;}
};
vector<mint> mint::fac;
vector<mint> mint::ifac;
bool mint::init=1;

int main(){
    lint n,k;
    cin>>n>>k;
    vec a(n);
    rep(i,n)cin>>a[i];
    vector<pair<fps9<mint>,fps9<mint>>>c(2*n-1);
    rep(i,n){
        c[i+n-1]=make_pair(fps9<mint>{1},fps9<mint>{1,-a[i]});
    }
    auto merge=[&](auto s,auto t){
        return make_pair(s.first*t.second+s.second*t.first,s.second*t.second);
    };
    rrep(i,n-1){
        c[i]=merge(c[i*2+1],c[i*2+2]);
    }
    auto e=(c[0].first*(c[0].second.inv(k+1))).pre(k+1);
    vector<mint> ans(k);
    rep(i,1,k+1){
        ans[i-1]=e[i];
    }
    output(ans);
}